If sin pi12 12 Squareroot A Squareroot B then by using a h

If sin pi/12 = 1/2 Squareroot A - Squareroot B, then, by using a half-angle formula, find A =, B = .

Solution

sin(/12)=sin(^(/6)/2)

sin(A/2)=[(1-cosA)/2]

sin(/12)=[(1-cos(/6))/2]

sin(/12)=[(1-((3)/2))/2]

sin(/12)=[((2-3)/2)/2]

sin(/12)=[(2-3)/4]

sin(/12)=(1/2)(2-3)

A=2

B=3